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How to use it?
- Integral of d{x}:
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Integral of 1/(2+x^2)
- Integral of sin(w*t)^2
- Integral of sin(log(x))^2/x
- Integral of sin^n(x)
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Identical expressions
- one /((x- four)*sqrt(x))
- 1 divide by ((x minus 4) multiply by square root of (x))
- one divide by ((x minus four) multiply by square root of (x))
- 1/((x-4)*√(x))
- 1/((x-4)sqrt(x))
- 1/x-4sqrtx
- 1 divide by ((x-4)*sqrt(x))
- 1/((x-4)*sqrt(x))dx
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Similar expressions
- 1/((x+4)*sqrt(x))
Integral of 1/((x-4)*sqrt(x)) dx
The solution
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[src]
25 / | | 1 | ------------- dx | ___ | (x - 4)*\/ x | / 4
$$\int\limits_{4}^{25} \frac{1}{\sqrt{x} \left(x - 4\right)}\, dx$$
Integral(1/((x - 4)*sqrt(x)), (x, 4, 25))
The answer (Indefinite)
[src]
// / ___\ \
|| |\/ x | |
||-acoth|-----| |
/ || \ 2 / |
| ||-------------- for x > 4|
| 1 || 2 |
| ------------- dx = C + 2*|< |
| ___ || / ___\ |
| (x - 4)*\/ x || |\/ x | |
| ||-atanh|-----| |
/ || \ 2 / |
||-------------- for x < 4|
\\ 2 /
$$\int \frac{1}{\sqrt{x} \left(x - 4\right)}\, dx = C + 2 \left(\begin{cases} - \frac{\operatorname{acoth}{\left(\frac{\sqrt{x}}{2} \right)}}{2} & \text{for}\: x > 4 \\- \frac{\operatorname{atanh}{\left(\frac{\sqrt{x}}{2} \right)}}{2} & \text{for}\: x < 4 \end{cases}\right)$$
The graph
Use the examples entering the upper and lower limits of integration.